id
string | setting_key
string | difficulty
string | level
int32 | messages
dict | ground_truth
string | dataset
string | omega_split
string |
|---|---|---|---|---|---|---|---|
math_algebra_func_area_level_2_2_900
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(-2(-1|x - 3| - 3) + 5) + 2, g(x) = (-1(-3cos(1πx - 1)) - 3)/(-2(-3cos(1πx - 1)) + 3), x = -1.0, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
43.4
|
math
|
train
|
math_algebra_func_area_level_2_2_901
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-3(1cos(1π(1x + 5) + 2) - 2) - 2)/(-1(1cos(1π(1x + 5) + 2) - 2) - 3) and g(x) = (1(-1e^(-1x) - 2) + 1)/(-1(-1e^(-1x) - 2)) from x = 4.3 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_902
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2((-2(3|x + 3| + 2))/(-3(3|x + 3| + 2) - 3))^2 - 1((-2(3|x + 3| + 2))/(-3(3|x + 3| + 2) - 3)) + 1, g(x) = -3cos(1π(-2|x - 3|) + 3) - 1, x = 4.1, and x = 4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.3
|
math
|
train
|
math_algebra_func_area_level_2_2_903
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|((-2(3|x - 1|) + 1)/(-2(3|x - 1|) - 1)) - 1| + 2, g(x) = -3(-4x - 1)^2 + 2(-4x - 1) + 3, x = -0.5, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_904
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(2sin(1π(-5x + 2) - 2) + 3) - 2| + 2, g(x) = 1(1cos(2πx + 3) - 1) + 2, x = 2.1, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_2_2_905
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-1(-5((-3x + 2)/(2x))^2 - 1((-3x + 2)/(2x))) + 1)/(-3(-5((-3x + 2)/(2x))^2 - 1((-3x + 2)/(2x))) - 3) and g(x) = (2(1x + 5) + 3)/(3(1x + 5) + 2) from x = 0.5 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.2
|
math
|
train
|
math_algebra_func_area_level_2_2_906
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(1((2x + 3)/(-1x))^2 - 5((2x + 3)/(-1x)) + 3) + 2| - 3 and g(x) = -1|((1x)/(-1x - 1)) + 2| - 3 from x = -1.2 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
54.8
|
math
|
train
|
math_algebra_func_area_level_2_2_907
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(2((-1x + 1)/(3x + 1))^2 + 5((-1x + 1)/(3x + 1)) - 2) + 1)/(1(2((-1x + 1)/(3x + 1))^2 + 5((-1x + 1)/(3x + 1)) - 2) - 3), g(x) = (-1(-2cos(2πx) + 3) + 1)/(-3(-2cos(2πx) + 3) - 2), x = -0.5, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
8.5
|
math
|
train
|
math_algebra_func_area_level_2_2_908
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1(3(-2x - 4) - 2) + 3)/(-2(3(-2x - 4) - 2) - 2) and g(x) = 2sin(1π(-4x^2 + 3x - 1)) - 1 between the vertical lines x = -3.2 and x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_909
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3(2|(1x - 3) + 1| - 1)^2 + 4(2|(1x - 3) + 1| - 1) + 1 and g(x) = 1cos(2π(-1|x + 2|) - 1) - 1 between the vertical lines x = 1.7 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_2_2_910
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2cos(3π(-2|(4x + 3) - 2| + 1) - 2) - 1, g(x) = 1(1x + 4) - 2, x = -1.5, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_911
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(2(5x^2 - 1x - 4)^2 + 5(5x^2 - 1x - 4) + 3), g(x) = (2(-4x^2 + 4x + 4) + 1)/(-3(-4x^2 + 4x + 4) + 4), x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_912
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(-4(-3x - 5)^2 + 1(-3x - 5)) - 2)/(2(-4(-3x - 5)^2 + 1(-3x - 5)) + 3), g(x) = -3e^(2(5x)) - 2, x = -1.8, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_913
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3cos(3π((-3(-2|x - 2| + 1) - 1)/(-3(-2|x - 2| + 1) - 2))) - 1, g(x) = (-3((-3x + 2)/(-1x - 2)) - 2)/(-1((-3x + 2)/(-1x - 2)) + 2), x = 1.1, and x = 1.2000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_914
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4((3((-1x - 1)/(-3x - 1)) - 2)/(-3((-1x - 1)/(-3x - 1)) - 3)) - 5 and g(x) = -3(-4x^2 + 5x + 3)^2 - 2(-4x^2 + 5x + 3) + 5 between the vertical lines x = 1.5 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.6
|
math
|
train
|
math_algebra_func_area_level_2_2_915
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1((1(2sin(3πx - 2)) - 1)/(-1(2sin(3πx - 2))))^2 - 4((1(2sin(3πx - 2)) - 1)/(-1(2sin(3πx - 2)))) + 2, g(x) = 1|(-1cos(2πx - 1) - 1) + 3| - 1, x = -0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.0
|
math
|
train
|
math_algebra_func_area_level_2_2_916
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1((1(-3cos(2πx + 2) - 2) - 2)/(3(-3cos(2πx + 2) - 2) + 3)) + 2)/(3((1(-3cos(2πx + 2) - 2) - 2)/(3(-3cos(2πx + 2) - 2) + 3)) - 2), g(x) = -1|((-2x + 3)/(-2x - 3)) + 3| + 2, x = -1.4, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_917
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-1(1sin(1π((-2x)/(-3x + 2)) - 2)) + 1)/(-2(1sin(1π((-2x)/(-3x + 2)) - 2)) + 1), g(x) = -4(2x + 5) - 1, x = -2.7, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
62.1
|
math
|
train
|
math_algebra_func_area_level_2_2_918
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1sin(3π(-5(4x - 5) + 5) - 2) - 1 and g(x) = 1((1x - 1)/(1x + 1))^2 - 4((1x - 1)/(1x + 1)) + 2 between the vertical lines x = -4.2 and x = -4.1000000000000005. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_919
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(1|(2cos(1πx - 1) - 3)| - 2) + 3 and g(x) = 1|(2x + 1) - 2| between the vertical lines x = 1.0 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.1
|
math
|
train
|
math_algebra_func_area_level_2_2_920
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(-3|(-1|x - 3|) + 3| + 3) - 2, g(x) = (1(-2cos(1πx + 1) + 3) + 1)/(-1(-2cos(1πx + 1) + 3) + 2), x = -2.7, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
41.2
|
math
|
train
|
math_algebra_func_area_level_2_2_921
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(-2(-2|x| - 1)^2 - 5(-2|x| - 1) - 3) + 2, g(x) = -2e^(-1(-2x + 2)) + 1, x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_2_2_922
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(3(-5x + 2) - 3) - 1 and g(x) = 3(2|x - 1| - 1)^2 - 2(2|x - 1| - 1) + 1 between the vertical lines x = 0.3 and x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
50.1
|
math
|
train
|
math_algebra_func_area_level_2_2_923
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(-1(2cos(2πx - 3) - 3)^2 - 1(2cos(2πx - 3) - 3) + 4)^2 - 4(-1(2cos(2πx - 3) - 3)^2 - 1(2cos(2πx - 3) - 3) + 4) + 3 and g(x) = 1(-2cos(3πx + 3) + 1) + 3 between the vertical lines x = 2.4 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_2_2_924
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(-3|(-3|x| + 2) - 2| + 2)^2 + 2(-3|(-3|x| + 2) - 2| + 2) - 5, g(x) = -3cos(2π(3x - 3) - 3) - 3, x = 0.2, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_925
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2(2e^(-2((-1x + 2)/(2x + 1))) - 2) - 3, g(x) = 3cos(3π(-5x) + 3) + 2, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_926
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (2(5(1|x + 2| - 2)^2 - 3))/(-1(5(1|x + 2| - 2)^2 - 3) - 1) and g(x) = -2e^(-2(-3x - 4)) - 3 from x = -4.0 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
41.4
|
math
|
train
|
math_algebra_func_area_level_2_2_927
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-3|((1x - 3)/(-2x - 1)) + 1| - 2))/(3(-3|((1x - 3)/(-2x - 1)) + 1| - 2) - 1), g(x) = -5(-2cos(1πx - 2) - 2)^2 + 4(-2cos(1πx - 2) - 2) + 4, x = -0.6, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_2_2_928
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3|((-1((-2x + 2)/(3x - 2)) + 2)/(-3((-2x + 2)/(3x - 2)) - 1)) + 2| - 3, g(x) = (-3(-5x^2 + 5x))/(-1(-5x^2 + 5x) + 3), x = 0.9, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_929
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3((1(3x - 3) - 3)/(-3(3x - 3) + 4))^2 - 2((1(3x - 3) - 3)/(-3(3x - 3) + 4)) - 3, g(x) = 3cos(1π((-3x + 3)/(-2x - 3)) - 1) - 3, x = -1.3, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_930
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-5(2|x + 3|) + 5) - 1, g(x) = -1|((1x)/(1x + 1)) - 2| + 2, x = -3.3, and x = -2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_2_2_931
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|(-3|(5x + 4) + 1| + 2) - 1| + 2 and g(x) = -3sin(1π(4x - 5) + 3) + 3 from x = -1.0 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_932
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (2(-2cos(1π((-1x + 3)/(-2x + 3)) + 1) - 1) + 1)/(2(-2cos(1π((-1x + 3)/(-2x + 3)) + 1) - 1) + 2), g(x) = (-1(1e^(2x) + 1) - 1)/(2(1e^(2x) + 1) + 1), x = 2.0, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.1
|
math
|
train
|
math_algebra_func_area_level_2_2_933
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-2(-3(2e^(1x))^2 - 3(2e^(1x)) + 2) - 1)/(3(-3(2e^(1x))^2 - 3(2e^(1x)) + 2) - 2), g(x) = -3cos(1π(1x^2 + 5x - 3)), x = 0.3, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_934
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1sin(2π(-1(1|x + 1| + 1) - 1)) + 2, g(x) = 2|(3|x - 3| - 3) - 1| + 1, x = 4.3, and x = 4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_935
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 4(-4(1|x + 3| - 1) - 3)^2 - 4(-4(1|x + 3| - 1) - 3) - 4 and g(x) = 1|(2x + 5) + 2| - 1 from x = -3.4 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.0
|
math
|
train
|
math_algebra_func_area_level_2_2_936
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(5(3sin(1πx - 1) - 1) - 4) - 2, g(x) = (-2(1|x + 2| + 2) - 3)/(-1(1|x + 2| + 2)), x = 3.1, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
67.4
|
math
|
train
|
math_algebra_func_area_level_2_2_937
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|((2(-4x - 5) + 1)/(-3(-4x - 5) - 2))| - 1 and g(x) = -1(1e^(1x) - 2)^2 - 2(1e^(1x) - 2) - 5 from x = -1.1 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_2_2_938
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(1(1x + 4) - 4) - 3)/(2(1(1x + 4) - 4) - 1) and g(x) = -2|(1|x + 3| + 3) - 3| + 3 between the vertical lines x = -3.9 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_2_2_939
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(2|((-3x + 3)/(2x + 3)) - 1| - 1)^2 - 5(2|((-3x + 3)/(2x + 3)) - 1| - 1) - 5, g(x) = -2cos(2π(-1|x - 3| - 1)) - 3, x = -0.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_2_2_940
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(3cos(3π((3x - 2)/(1x)) + 2)) + 2)/(2(3cos(3π((3x - 2)/(1x)) + 2)) + 2), g(x) = 2|(-2e^(1x) + 2) + 3|, x = 0.1, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_2_2_941
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2sin(2π(1(1|x + 1| - 2)^2 - 3(1|x + 1| - 2) + 5) - 1) + 3 and g(x) = -3(3x - 5) - 1 between the vertical lines x = 1.1 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_942
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1((-1((3x + 1)/(2x - 1)))/(-1((3x + 1)/(2x - 1)) - 2)) - 1 and g(x) = -5(3cos(3πx + 1) - 1) + 2 from x = 2.5 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
math_algebra_func_area_level_2_2_943
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1sin(2π((-1(2|x - 1| - 1) - 3)/(-2(2|x - 1| - 1) - 3)) + 3) - 3 and g(x) = -2|(-3x - 1)| + 1 from x = -0.9 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_2_2_944
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -3(-5(-5x - 1)^2 + 3(-5x - 1)) - 5, g(x) = 1|((-2x - 1)/(-2x - 3)) - 1|, x = -0.4, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_2_2_945
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(-3(-1x + 5) + 2)^2 + 2(-3(-1x + 5) + 2) - 2 and g(x) = (3(-3sin(2πx + 1) - 1))/(-2(-3sin(2πx + 1) - 1) - 1) between the vertical lines x = 3.8 and x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_2_2_946
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2(-5(2sin(1πx))^2 + 5(2sin(1πx)) + 2) - 1, g(x) = -3|((2x - 2)/(-3x)) + 2| + 2, x = 0.8, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.4
|
math
|
train
|
math_algebra_func_area_level_2_2_947
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(1(5x - 4)^2 - 1(5x - 4)), g(x) = (1(-1cos(3πx - 2) + 2) + 2)/(2(-1cos(3πx - 2) + 2) + 3), x = 0.8, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_948
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 3(-3|(-4x^2 + 5)|)^2 + 3(-3|(-4x^2 + 5)|) - 4, g(x) = 1((2x)/(-3x + 2))^2 + 1((2x)/(-3x + 2)) + 5, x = 0.7, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.9
|
math
|
train
|
math_algebra_func_area_level_2_2_949
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2sin(3π(1((-1x - 3)/(1x - 2)) + 4) - 2) - 3 and g(x) = -1(1e^(1x) + 3) + 3 between the vertical lines x = 1.6 and x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_950
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(2|(-2cos(3πx + 2) - 1) + 1|) - 1 and g(x) = -1(3e^(-2x) - 3)^2 - 5(3e^(-2x) - 3) - 5 between the vertical lines x = 1.3 and x = 1.4000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_2_2_951
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 2cos(2π(-1(-2|x - 3| - 2)^2 + 3(-2|x - 3| - 2) - 3) - 1) + 3 and g(x) = (2((2x + 3)/(-1x - 2)) + 2)/(-2((2x + 3)/(-1x - 2)) + 3) from x = -1.6 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_952
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3(2cos(1π(-1x + 5) + 2) - 2) - 1 and g(x) = 2|(2x) - 3| - 3 between the vertical lines x = 4.3 and x = 4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.5
|
math
|
train
|
math_algebra_func_area_level_2_2_953
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -2|((1(-3|x + 1|))/(1(-3|x + 1|) - 3)) + 2| + 2 and g(x) = (-1(-3x^2 - 1x + 4) + 3)/(1(-3x^2 - 1x + 4) + 1) between the vertical lines x = -1.7 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
23.4
|
math
|
train
|
math_algebra_func_area_level_2_2_954
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1|((-2(3x + 3) - 3)/(2(3x + 3) - 3)) + 3| - 1 and g(x) = 4(2x^2 + 1x - 1) - 4 from x = -0.4 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.6
|
math
|
train
|
math_algebra_func_area_level_2_2_955
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 5((3(-2|x + 3| + 1) - 1)/(-3(-2|x + 3| + 1) - 2)) + 2 and g(x) = 5(-3cos(3πx + 3) - 1)^2 - 2(-3cos(3πx + 3) - 1) + 1 between the vertical lines x = -3.8 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
14.2
|
math
|
train
|
math_algebra_func_area_level_2_2_956
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (3(5(2x^2 - 3x - 5)^2 - 3(2x^2 - 3x - 5) - 5) - 2)/(2(5(2x^2 - 3x - 5)^2 - 3(2x^2 - 3x - 5) - 5) + 2) and g(x) = -3e^(2(-4x - 3)) + 1 from x = 2.3 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.9
|
math
|
train
|
math_algebra_func_area_level_2_2_957
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1((-2(2x^2 - 3x - 5) + 2)/(-1(2x^2 - 3x - 5) - 1)) + 3 and g(x) = -4(2cos(1πx) + 2)^2 + 4(2cos(1πx) + 2) + 5 from x = -4.6 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
27.7
|
math
|
train
|
math_algebra_func_area_level_2_2_958
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 5(3(3x + 5)^2 + 2(3x + 5) - 2) - 5, g(x) = (-3(3x - 4) + 3)/(-2(3x - 4) - 1), x = -2.2, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.2
|
math
|
train
|
math_algebra_func_area_level_2_2_959
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 4(1(-1e^(-1x) + 3)^2 + 4(-1e^(-1x) + 3) - 2)^2 + 5(1(-1e^(-1x) + 3)^2 + 4(-1e^(-1x) + 3) - 2) - 5 and g(x) = 4(-2x - 4) + 3 between the vertical lines x = -1.9 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
53.6
|
math
|
train
|
math_algebra_func_area_level_2_2_960
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (1(-1|(3sin(3πx - 3) + 1) + 2| + 2) - 1)/(-3(-1|(3sin(3πx - 3) + 1) + 2| + 2) + 4), g(x) = 1|(1cos(3πx + 2) + 3) + 3| + 2, x = 3.6, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.2
|
math
|
train
|
math_algebra_func_area_level_2_2_961
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(1(2sin(2πx))^2 - 5(2sin(2πx)) + 5)^2 - 3(1(2sin(2πx))^2 - 5(2sin(2πx)) + 5) + 3 and g(x) = -1(-2|x - 3| + 3)^2 - 5(-2|x - 3| + 3) + 5 between the vertical lines x = -0.5 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
75.7
|
math
|
train
|
math_algebra_func_area_level_2_2_962
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(-5(-1x^2 - 2x + 5)^2 - 2(-1x^2 - 2x + 5) + 1)| and g(x) = -2|(-4x^2 + 4x + 5) + 1| + 3 from x = 1.6 to x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.7
|
math
|
train
|
math_algebra_func_area_level_2_2_963
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -1(2cos(3π(1x^2 - 1x - 1) + 1) - 2) + 1 and g(x) = -3e^(-2(3|x - 1| - 1)) + 3 from x = -4.0 to x = -3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_964
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -2(-3cos(1π((-3x - 1)/(3x - 2)) - 1)) - 5 and g(x) = -2sin(2π(1x + 2) + 2) - 1 from x = -0.3 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_2_2_965
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (-2(-2((1x - 1)/(1x + 2))^2 - 1((1x - 1)/(1x + 2)) + 2) + 2)/(2(-2((1x - 1)/(1x + 2))^2 - 1((1x - 1)/(1x + 2)) + 2) + 1) and g(x) = -1sin(3π(1|x + 2| + 3)) - 2 between the vertical lines x = -2.2 and x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_966
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 2(-1(1e^(-2x) + 1) + 5)^2 - 1(-1(1e^(-2x) + 1) + 5) + 4, g(x) = 3e^(-1(1x^2 - 2x - 1)) + 3, x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_967
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (2(-4((-2x - 2)/(1x)) - 4) - 3)/(1(-4((-2x - 2)/(1x)) - 4)) and g(x) = 3|(-3|x| + 2)| + 2 between the vertical lines x = -1.9 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.0
|
math
|
train
|
math_algebra_func_area_level_2_2_968
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(-3sin(3π(-1x^2 + 1x + 4) - 3)) + 4, g(x) = (1(3x + 5) - 3)/(3(3x + 5) + 2), x = -2.2, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_969
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -4((3(2x + 4) - 1)/(-1(2x + 4) - 1))^2 - 3((3(2x + 4) - 1)/(-1(2x + 4) - 1)) + 4, g(x) = 3cos(1π(-3x - 5) + 1) + 2, x = -1.4, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_970
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (-2(5(-3|x - 1| + 1)) - 3)/(3(5(-3|x - 1| + 1))) and g(x) = (1((-3x + 3)/(-2x)))/(-2((-3x + 3)/(-2x)) - 1) from x = 0.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.3
|
math
|
train
|
math_algebra_func_area_level_2_2_971
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2(-3sin(3π(1|x + 1| - 1) + 3) - 2) + 5 and g(x) = (1(-1x - 2) + 1)/(1(-1x - 2)) between the vertical lines x = -3.4 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.6
|
math
|
train
|
math_algebra_func_area_level_2_2_972
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5((2((-3x + 3)/(3x - 1)) + 1)/(3((-3x + 3)/(3x - 1)))) - 4 and g(x) = 3(3|x + 1| - 3)^2 - 3(3|x + 1| - 3) - 2 from x = 0.5 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.3
|
math
|
train
|
math_algebra_func_area_level_2_2_973
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1sin(1π(2(1|x + 1| - 1)^2 + 4(1|x + 1| - 1) - 2) + 2) - 3 and g(x) = -5(2x - 1)^2 - 5(2x - 1) - 2 from x = -0.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_2_2_974
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1((-1((-2x + 1)/(-2x + 3)) - 3)/(-2((-2x + 1)/(-2x + 3)) - 2)) + 4 and g(x) = (-2(2x) + 2)/(2(2x) + 1) between the vertical lines x = -0.1 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
11.6
|
math
|
train
|
math_algebra_func_area_level_2_2_975
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1(2sin(3π(1x - 2) - 3))^2 - 1(2sin(3π(1x - 2) - 3)) + 5 and g(x) = -3(-2sin(2πx) - 1)^2 + 4(-2sin(2πx) - 1) + 3 between the vertical lines x = -2.1 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
13.3
|
math
|
train
|
math_algebra_func_area_level_2_2_976
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3sin(3π(-3(-2|x - 1| - 1) + 1) + 2) + 1 and g(x) = 3(-2|x - 1| + 3) + 2 from x = -0.3 to x = -0.19999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_977
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1sin(2π(-1((1x + 3)/(1x)) + 2) + 2), g(x) = -1|(3e^(1x) - 3) - 3| + 1, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_978
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 4(1(4x - 1)) + 2, g(x) = (3(1|x| - 3) - 3)/(2(1|x| - 3) - 1), x = 0.2, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
95.9
|
math
|
train
|
math_algebra_func_area_level_2_2_979
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (1((2(2x + 3))/(-2(2x + 3) - 2)) + 3)/(-1((2(2x + 3))/(-2(2x + 3) - 2)) + 2) and g(x) = -3e^(-1((3x + 3)/(1x + 3))) + 3 between the vertical lines x = -1.8 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.7
|
math
|
train
|
math_algebra_func_area_level_2_2_980
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(1|(-1|x - 1| + 2) + 3| + 1)^2 - 5(1|(-1|x - 1| + 2) + 3| + 1) + 5 and g(x) = 5(2|x - 2| - 1) + 3 from x = 0.8 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
6.8
|
math
|
train
|
math_algebra_func_area_level_2_2_981
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -3|(-2cos(2π(-5x - 1)) - 2) - 1| - 1 and g(x) = -4(-2|x| + 3)^2 + 1(-2|x| + 3) + 4 from x = 2.3 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_982
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 1(4(-1|x - 2| + 2) - 5) + 2 and g(x) = (-2((1x - 1)/(-2x + 3)) + 3)/(2((1x - 1)/(-2x + 3)) - 3) from x = 0.5 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
9.0
|
math
|
train
|
math_algebra_func_area_level_2_2_983
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(2|(-3sin(2πx) - 2) + 1| - 3) - 2)/(2(2|(-3sin(2πx) - 2) + 1| - 3)) and g(x) = 1e^(-2((2x - 1)/(-2x + 1))) from x = 1.6 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.6
|
math
|
train
|
math_algebra_func_area_level_2_2_984
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = (1(-1|(1x^2 - 4x - 2) + 3| + 2) + 3)/(-1(-1|(1x^2 - 4x - 2) + 3| + 2) - 3) and g(x) = 2sin(2π(1x + 1) - 1) - 1 from x = -4.8 to x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.6
|
math
|
train
|
math_algebra_func_area_level_2_2_985
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -3|(-3|(1x^2 - 3x + 1) + 1| - 3)| - 3 and g(x) = 4(-2|x + 1| - 2) between the vertical lines x = 0.4 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
36.9
|
math
|
train
|
math_algebra_func_area_level_2_2_986
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -2|(-3|(3|x + 1| - 1) + 2| + 3) + 1| + 2, g(x) = (-2(1x + 4) + 3)/(-1(1x + 4) - 1), x = -1.0, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_987
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = (3(-1cos(1π(1x - 4)) + 3) + 1)/(3(-1cos(1π(1x - 4)) + 3) + 3) and g(x) = 2(-4x^2 + 4x - 2) + 3 between the vertical lines x = 0.4 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.0
|
math
|
train
|
math_algebra_func_area_level_2_2_988
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = 1(-4(-1|x + 3| + 1) - 5) - 2, g(x) = 5(4x^2 + 4x - 5)^2 - 3(4x^2 + 4x - 5) - 4, x = 0.6, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.5
|
math
|
train
|
math_algebra_func_area_level_2_2_989
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = -1|(-3|(-3x - 2)| - 2) - 2| + 1 and g(x) = -2|(-1x - 4)| - 3 between the vertical lines x = -1.3 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
5.2
|
math
|
train
|
math_algebra_func_area_level_2_2_990
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = (-3(-2|(-1|x + 1| + 1) - 1| + 2) + 2)/(-1(-2|(-1|x + 1| + 1) - 1| + 2) + 3), g(x) = -2e^(1(-1x^2 - 5x + 3)) + 2, x = 0.7, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.2
|
math
|
train
|
math_algebra_func_area_level_2_2_991
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = -4(1(-1|x + 2| - 2)^2 + 3(-1|x + 2| - 2) - 2) - 3 and g(x) = -2((-2x - 1)/(-3x + 1))^2 + 4((-2x - 1)/(-3x + 1)) + 4 from x = 0.1 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
-14.9
|
math
|
train
|
math_algebra_func_area_level_2_2_992
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -1(3|(1x + 5) - 1| - 1) + 2, g(x) = -1cos(3π(-1x^2 - 4x + 5) - 2) + 1, x = -5.0, and x = -4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.1
|
math
|
train
|
math_algebra_func_area_level_2_2_993
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 3sin(3π(5(3x + 1)^2 + 1(3x + 1) + 2) + 2) - 3 and g(x) = 2(5x^2 + 2x - 1) + 2 between the vertical lines x = -0.1 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.3
|
math
|
train
|
math_algebra_func_area_level_2_2_994
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3|(2|(2sin(3πx + 3) - 1) + 2| - 2) - 2| - 1 and g(x) = (-2(-2sin(3πx - 2) + 1) - 2)/(-1(-2sin(3πx - 2) + 1) - 2) from x = -1.4 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
2.3
|
math
|
train
|
math_algebra_func_area_level_2_2_995
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Find the area of the region bounded by the curves f(x) = -5(2(2|x + 1| - 1)^2 + 5(2|x + 1| - 1))^2 - 3(2(2|x + 1| - 1)^2 + 5(2|x + 1| - 1)) - 4, g(x) = 3(-3|x + 3| - 1) - 1, x = -1.2, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
4.2
|
math
|
train
|
math_algebra_func_area_level_2_2_996
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 5((2(-3|x| + 1) + 2)/(3(-3|x| + 1) - 2))^2 + 4((2(-3|x| + 1) + 2)/(3(-3|x| + 1) - 2)) - 3 and g(x) = 2|(-3x + 5) + 3| - 2 from x = 0.2 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
15.9
|
math
|
train
|
math_algebra_func_area_level_2_2_997
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 2|((1(5x + 5))/(2(5x + 5)))| + 1 and g(x) = -4(-2e^(1x) + 2)^2 - 2(-2e^(1x) + 2) + 4 between the vertical lines x = -0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
1.0
|
math
|
train
|
math_algebra_func_area_level_2_2_998
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Calculate the area enclosed between the functions f(x) = 3(2|(3|x - 1| - 2) + 3| - 3) and g(x) = 5(-2|x - 2| - 1)^2 - 5(-2|x - 2| - 1) - 4 from x = 1.8 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
3.0
|
math
|
train
|
math_algebra_func_area_level_2_2_999
|
algebra_func_area2
|
medium (level 2,3)
| 2 |
{
"role": [
"user"
],
"content": [
"Determine the area of the region enclosed by the graphs of f(x) = 1(3(-2cos(2πx + 2) - 2) + 4) and g(x) = (1(5x + 2) - 3)/(2(5x + 2)) between the vertical lines x = 3.0 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
]
}
|
0.9
|
math
|
train
|
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